Mr Hickman's Class 2022-2023
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images taken from https://apcentral.collegeboard.org

What is a Derivative?

Types of Problems:

  • Defining Average and Instantaneous Rates of Change at a Point
  • Defining a Derivative of a Function and using Derivative Notation
  • Estimating Derivatives of a Function at a Point

Notes & Handouts

Practice 

Video and other resources

Digital Resources

Desmos Files
(these files investigate the following)
  • Instantaneous rate of change at a given point
  • Slope of tangent line for a function at a given point
  • Linear function y = x
  • Quadratic Function y=x^2
  • ​Cubic Function y=x^3
  • Square Root Function
  • ​Cube Root Function
  • Rational Function y =1/x

Connecting Differentiability and Continuity

Types of Problems:

  • What does it mean to be differentiable?
  • What does it mean to be continuous?
  • Determining when derivatives do and do not exist

Notes & Handouts

Practice

​Video and other resources

​Digital Resources


Power Rule for Derivatives

​Types of Problems:

  • Using Power Rule to determine the derivative at a point
  • Proving the Power Rule with the use of limits and limit properties

​Practice

​Video and other resources

​Notes & Handouts

​​Digital Resources

Desmos Files
(these files investigate the following)
  • Instantaneous rate of change at a given point
  • Slope of tangent line for a function at a given point
  • Linear Functions (slope intercept form)
  • Quadratic Function in standard form 
  • ​Cubic Function in standard form​

Basic Rules for Differentiation

​Types of Problems:

  • Using Constant Rule to determine the derivative at a point
  • Proving the Constant Rule with the use of limits and limit properties
  • Using Sum or Difference Rule to determine the derivative at a point
  • Proving the Sum and Difference Rules with the use of limits and limit properties
  • Using Constant Multiple Rule to determine the derivative at a point
  • Proving the Constant Multiple Rule with the use of limits and limit properties

​Practice

​Video and other resources

​Notes & Handouts

​Digital Resources


Derivatives of cos x, sin x, b^x, e^x, log b x, and ln x

​​Types of Problems:

  • Using Cosine Derivative Rule to determine the derivative at a point
  • Using Sine Derivative Rule to determine the derivative at a point
  • Using Derivative of e^x Rule to determine the derivative at a point
  • Using Derivative of ln x Rule to determine the derivative at a point

​​Notes & Handouts

​​Practice

​Video and other resources

​Digital Resources

​Desmos Files
(these files investigate the following)
  • Instantaneous rate of change at a given point
  • Slope of tangent line for a function at a given point
  • Exponential Functions base b 
  • Exponential Functions base e
  • Logarithmic Functions base b
  • Logarithmic Functions base e

Product and Quotient Rule

​​Types of Problems:

  • Using Product Rule to determine the derivative at a point
  • Using Quotient Rule to determine the derivative at a point
  • Using Negative Exponents to use Product Rule instead of Quotient Rule

​​Practice

​Video and other resources

​​Notes & Handouts

​Digital Resources


Derivatives of tan x, cot x,  sec x, and csc x

​​​Types of Problems:

  • Using Tangent Derivative Rule to determine the derivative at a point
  • Using Cotangent Derivative Rule to determine the derivative at a point
  • Using Secant Derivative Rule Rule to determine the derivative at a point
  • Using Cosecant Derivative Rule to determine the derivative at a point

​​​Notes & Handouts

​​​Practice

​​Video and other resources

​​Digital Resources

​

Additional Resources

Professor Leonard's You Tube Channel ​

Paul's Online Notes for Calc 1

Overview of Topics

KHAN Academy: Derivatives

​​CK 12 Link: Derivatives



Mr Hickman is available for assistance after school practically anytime.  Talk to me to be certain that I am aware you are coming and 99% of the time I will be able to help you